The coin in the JJH posts is dated 1814: the Gumph coin, according to the poster, is "a coronet head large cent which were minted between 1816 - 1839." But they sure look identical, though with very different amounts of wear. Good catch, Rob!
I know nothing about counterstamps or about coins. But I will add here, as I said in the JJH post, that that 1814 coin would not have been stamped "J. J. Henry / Boulton" in 1814. Perhaps in 1822 and after, when J. J. Henry took over Boulton--which, earlier, had been a joint operation between him and his brother and the stamps reflected that (J. & W. Henry, typically). In 1814, J. J. Henry was working as a gunsmith in Philadelphia.